//不同路径 III
//测试链接：https://leetcode.cn/problems/unique-paths-iii/
public class UniquePathsIII {
    boolean[][] vis;
    int m, n, step;
    int ret;
    int[] dx = { 0, 0, 1, -1 };
    int[] dy = { 1, -1, 0, 0 };

    public int uniquePathsIII(int[][] grid) {
        m = grid.length;
        n = grid[0].length;
        vis = new boolean[m][n];
        int bx = 0, by = 0;
        for (int i = 0; i < m; i++)
            for (int j = 0; j < n; j++)
                if (grid[i][j] == 0)
                    step++;
                else if (grid[i][j] == 1) {
                    bx = i;
                    by = j;
                }
        step += 2;
        vis[bx][by] = true;
        dfs(grid, bx, by, 1);
        return ret;
    }

    public void dfs(int[][] grid, int i, int j, int count) {
        if (grid[i][j] == 2) {
            if (count == step) {
                ret++;
            }
            return;
        }
        for (int k = 0; k < 4; k++) {
            int x = i + dx[k], y = j + dy[k];
            if (x >= 0 && x < m && y >= 0 && y < n && !vis[x][y] && grid[x][y] != -1) {
                vis[x][y] = true;
                dfs(grid, x, y, count + 1);
                vis[x][y] = false;
            }
        }
    }
}
